In order to enable a better understanding of the key concepts of automation, this book develops the fundamental aspects of the field while also proposing numerous concrete exercises and their solutions. The theoretical approach that it presents fundamentally uses the state space and makes it possible to process general and complex systems in a simple way, involving several switches and sensors of different types. This approach requires the use of developed theoretical tools such as linear algebra, analysis and physics, generally taught in preparatory classes for specialist engineering courses.

In order to enable a better understanding of the key concepts of automation, this book develops the fundamental aspects of the field while also proposing numerous concrete exercises and their solutions. The theoretical approach that it presents fundamentally uses the state space and makes it possible to process general and complex systems in a simple way, involving several switches and sensors of different types. This approach requires the use of developed theoretical tools such as linear algebra, analysis and physics, generally taught in preparatory classes for specialist engineering courses.

INTRODUCTION viiCHAPTER 1. MODELING 11.1. Linear systems 11.2. Mechanical systems 21.3. Servomotors 41.4. Exercises 41.5. Solutions 21CHAPTER 2. SIMULATION 472.1. Concept of vector field 472.2. Graphical representation 492.2.1. Patterns 502.2.2. Rotation matrix 502.2.3. Homogeneous coordinates 522.3. Simulation 542.3.1. Euler's method 542.3.2. Runge-Kutta method 552.3.3. Taylor's method 562.4. Exercises 562.5. Solutions 67CHAPTER 3. LINEAR SYSTEMS 853.1. Stability 853.2. Laplace transform 873.2.1. Laplace variable 873.2.2. Transfer function 883.2.3. Laplace transform 883.2.4. Input-output relation 903.3. Relationship between state and transfer representations 903.4. Exercises 923.5. Solutions 103CHAPTER 4. LINEAR CONTROL 1274.1. Controllability and observability 1284.2. State feedback control 1294.3. Output feedback control 1304.4. Summary 1334.5. Exercises 1344.6. Solutions 150CHAPTER 5. LINEARIZED CONTROL 1855.1. Linearization 1855.1.1. Linearization of a function 1855.1.2. Linearization of a dynamic system 1875.1.3. Linearization around an operating point 1875.2. Stabilization of a nonlinear system 1885.3. Exercises 1915.4. Solutions 207BIBLIOGRAPHY 235INDEX 237